As \(S_2(\rho _B)=(1-|\mathbf {r}_B|^2)\) , we obtain the following
computable expression: \(I(\rho _{AB})=\lambda _{min} S_2(\rho _B)\) .
Note that a local filtering operation of the form
\(\rho ^{\prime }_{AB}=\frac{(I\otimes B)\rho _{AB}(I\otimes B^\dag )}{\textrm {Tr}[(I\otimes B^\dag B)\rho _{AB}]}\)  leaves
\(\mathbf {L}\)  invariant and transforms
\(S_2(\rho _{B^{\prime }})=\frac{\textrm {det}(B)^2}{\textrm {Tr}[(I\otimes B^\dag B)\rho _{AB}]^2}S_2(\rho _{B})\)  [1]}.
